# Number & Operations in Base Ten

Understanding how the different addition and subtraction strategies work is a second grade, Common Core math skill: 2.NBT.9. Below we show two videos that demonstrate this standard. Then, we provide a breakdown of the specific steps in the videos to help you teach your class.

Prior Learnings

Your students should be familiar with the first grade skill of counting up to 120 starting from any number below 120 (1.NBT.1), this skill helps them understand greater or less than values. The second grade skill is also closely linked to the first grade skill of understanding place values (ones and tens) in two-digit numbers (1.NBT.2).

Future Learnings

Comparing large numbers as greater than, less than, and equal to will help your students understand future concepts in third grade. In third grade, your students will learn how to interpret the products of whole numbers (i.e. 8 x 3 is the same as 8 groups of 3 objects each) (3.OA.1). They will also learn to use multiplication and division within 100 while solving word problems in situations that involve “equal groups, arrays, and measurement quantities” (3.OA.3).

Common Core Standard: 2.NBT.9 - Explain why addition and subtraction strategies work (place value and the properties of operations)

Students who understand this principle can:

1. Explain why strategies work using place value.
2. Apply properties of addition and subtraction to problems.
3. Explain why the addition and subtraction strategies work.

Video 1: Two Ways to Add

This video presents and breaks down two methods for solving the same addition problem. The problem used in the video is 48 + 26.

The first method follows the standard pattern of placing the digits in a column form and adding the numbers in the ones place first, then adding the numbers in the tens place.

1. In 48 + 26, first add 8 and 6.
2. 8 + 6 = 14
a. But we can’t write 14 below as only one number can fit in each place value.
b. So we write 4 in the answer slot and bring 1 up to the tens.
3. Next we add the tens column, 1 + 4 + 2 = 7.
4. Now we have the answer, 48 + 26 = 74.

Next, the video shows another method for solving the same problem by breaking the numbers up into tens and ones, using expanded form.

1. The first number (48) can be broken up into 40 + 8.
2. The second number (26) can be broken up into 20 + 6.
3. Now, we have a new addition statement that might be easier to add.
4. 8 + 6 = 14 and 40 + 20 = 60.
5. Now we have 60 + 14, which can be broken down even further.
a. 14 is also 10 + 4.
b. So, 60 + 10 = 70.
c. And 70 + 4 = 74.
6. Therefore, 48 + 26 = 74.

Both methods lead to the same answer, but they take different routes to arrive there.

Video 2: Find and Create Fact Families!

This video discusses fact families. A fact family explains 4 facts that show the relationship between addition and subtraction. Here’s an example:

• 1 + 2 = 3 and 2 + 1 = 3
o These are related addition facts.
• 3 - 2 = 1 and 3 - 1 = 2
o These are related subtraction facts.
• Fact families only use 3 numbers.

Boddle then moves onto some practice problems to help students better understand. Students must choose the correct related addition or subtraction facts from a list.

1. What’s the related fact for 8 + 3 = 11?
b. It’s 3 + 8 = 11.
2. What’s the related fact for 13 + 4 = 17?
a. All the other options have different numbers.
b. So, it’s 4 + 13 = 17.
3. What’s the related fact for 11 - 8 = 3?
a. Switch the second number (8) and the difference (3) to find the answer.
b. It’s 11 - 3 = 8.
4. What’s the related fact for 17 - 4 = 13?
a. Switch the second number and the difference to find the answer.
b. It’s 17 - 13 = 4.

Next, Boddle has students try one last exercise. From the facts written on 8 balloons, students must create 2 fact families by properly grouping the balloons.

1. Fact Family #1:
a. 10 + 9 = 19 and 9 + 10 = 19
b. 19 - 10 = 9 and 19 - 9 = 10
2. Fact Family #2:
a. 6 + 7 = 13 and 7 + 6 = 13
b. 13 - 7 = 6 and 13 - 6 = 7

That’s the end of this lesson; see you next time!

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